{
  "abstract": "A conjecture of Berger says that on a simply connected manifold all of whose geodesics are closed, all unit speed geodesics have the same shortest period. In this paper we will show that the S^1-action induced by the geodesic flow is free. We use symplectic geometry to investigate the topology of the quotient of the unit tangent bundle T^1M/S^1 by the S^1 action that comes from the geodesic flow. We show that this quotient admits the structure of a smooth symplectic manifold and that this symplectic manifold is symplectomorphic to S^2 \\times S^2 equipped with a split form. This will enable a computation involving the Euler class of the orbibundle T^1M\\rightarrow T^1M/S^1 which will lead to a solution of Berger's conjecture for three-dimensional manifolds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41006",
  "author_total": 1,
  "authors": [
    {
      "name": "Jakob Dittmer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fs1hqawkbj73s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41006",
  "fulltext_url": null,
  "id": "fs1hqawkbj73s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41006",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.SG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41006",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fs1hqawkbj73s.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41006",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41006"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Berger conjecture for three dimensional manifolds",
  "title_text": "The Berger conjecture for three dimensional manifolds",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/fs1hqawkbj73s",
  "venue": "arXiv",
  "versions": []
}